Vector space and subspaces

Question

So I know you can't have a empty vector space as if $V=\emptyset$ there is no zero vector anyway, and that you could have a empty subset of a vector space (as {$\emptyset$} subset of any set), but how come a empty subset of a vector space could also be a subspace? And how is $\operatorname{Lin}(\emptyset)=\{0\}$? I'm confused, sorry if my question is basic , Thanks.

Answer 1

The empty set is not a vector space, since $(\emptyset,+)$ has no identity element.